Divide through the limand by the highest power of t :
[tex]\displaystyle \lim_{t\to\infty} \frac{t^3-t+2}{(2t-1)(t^2+t+1)} = \lim_{t\to\infty} \frac{1 - \frac1{t^2} + \frac2{t^3}}{\left(2-\frac1t\right) \left(1+\frac1t + \frac1{t^2}\right)}[/tex]
(I distributed 1/t³ in the denominator as 1/t (2t - 1) and 1/t² (t² + t + 1).)
As to goes to infinity, these 1/tⁿ terms will converge to 0, and you're left with
[tex]\displaystyle \lim_{t\to\infty} \frac{1 - \frac1{t^2} + \frac2{t^3}}{\left(2-\frac1t\right) \left(1+\frac1t + \frac1{t^2}\right)} = \frac{1 - 0 + 0}{(2-0)(1+0+0)} = \boxed{\frac12}[/tex]
Find the area of the figure. Round to the nearest TENTH.
Answer:
Step-by-step explanation:
12 multiplied by 9 is 108. That gives us the square. The triangle base is 9. The height is 7. 7 multiplied by 9 is 63. 63 divided by 2 is 31.5. 108 add 31.5 is 139.5 cm squared.
Answer:
A=L*B
=12*9
=108
A=0.5base *H
=0.5(9)*7
=31.5
A=108+31.5
A=139.5
What are the coordinates for D?
options:
(-3, 2)
(-3, -1)
(-2, -3)
(-3, -2)
Answer:
(-3, -2)
Explanation:
Coordinates are represented in the form of (x, y)
To know the x coordinates see the value on the x-axis.
To know the y coordinates see the value on the y-axis.
From there we can identify:
A = (x, y) = (-4, 4)
B = (x, y) = (2, 2)
C = (x, y) = (0, -5)
D = (x, y) = (-3, -2) ← Required answer.
Find the surface area of the square pyramid.
A) 35 ft^2
B) 30 ft^2
C) 45 ft^2
D) 20 ft^2
Area of base
side²5²25ft²Area of one triangle side
1/2(2)(5)=5ft²Area of 4 sides
5(4)=20ft²TSA
20+25=45ft²
Answer:
C) 45 ft²
Step-by-step explanation:
Formulae
Area of a square = x² (where x is the side length)
Area of a triangle = 1/2 × base × height
The surface area of a square pyramid comprises:
square base4 congruent triangles⇒ area of square base = 5² = 25 ft²
⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²
⇒ Total surface area = area of square base + 4 triangular areas
= 25 + 4(5)
= 25 + 20
= 45 ft²
please help!!
I attached a picture!
HELP QUICK ILL GIVE BRAINLEST
Answer:
C) 15, 20, 25
Step-by-step explanation:
If you plug this in pythagorean theorem, it works. The others don't.
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Answer:
i think its D.
Step-by-step explanation:
i just counted
GIRL NO!!!! IM FAILING CAN SOMEONE HELP ME ASAP ON THIS SCREEN SHOT
Answer:
d = 306 m
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (10, 20) and (x₂, y₂ ) = (280, 164) ← house and beach coordinates
d = [tex]\sqrt{(280-10)^2+(164-20)^2}[/tex]
= [tex]\sqrt{270^2+144^2}[/tex]
= [tex]\sqrt{72900+20736}[/tex]
= [tex]\sqrt{93636}[/tex]
= 306 m
Answer:
The distance from Francesca's house to the beach is 306 meters.
Step-by-step explanation:
Use the Pythagorean Theorem to find the straight-line distance from Francesca's house to the beach.
Step 1 Find the length of the horizontal leg.
The length of the horizontal leg is the absolute value of the difference between the x- coordinates of the points (280,20) and (10,20).
|280 - 10| = 270
The length of the horizontal leg is 270 meters
Step 2 Find the length of the vertical leg.
The length of the vertical leg is the absolute value of the difference between the y- coordinates of the points (280,164) and (280,20)
|164 - 20| = 144
The length of the vertical leg is 144 meters.
Step 3 Let a = 270 and b = 144. Let c represent the length of the hypotenuse. Use the Pythagorean Theorem to find c.
a² + b² = c²
270² + 144² = c² Substitute into the formula.
72900 + 20736 = c² Simplify.
93636 = c² Add.
√93636 = c Take the square root of both sides.
306 = c Simplify.
The distance from Francesca's house to the beach is 306 meters.
Find the value of x.
31.5
68.3
26.7
11.
Answer:
26.7
Step-by-step explanation:
Using trigonometric ratio, we find:[tex]\sin 67\degree= \frac{x}{29}[/tex][tex]\implies x = 29\sin 67\degree[/tex][tex]\implies x =26.69464075[/tex][tex]\implies x \approx 26.7[/tex]what is -7/6 simplified
-7/6 = - 1.167 in simplest form
Answer:
Step-by-step explanation:
You cant simply this into fraction but you can simplify it to decimal form
which is - 1.17 round off
please help me I will give brainliest
Answer:
D
Step-by-step explanation:
um well just based on what its asking for it wants a sentence that uses both.
One winter day, the temperature ranged from a high of 20F to a low of -2F. By how many degrees did the temperature change?
Answer:
22 degrees F
Step-by-step explanation:
[tex]20--2=20+2[/tex]
Subtracting a negative number makes the sign positive, so 20 + 2 = 22 degrees F.
PLS HELLLLP!!!!!!!! I need 10 people to answer within the next 20 minutes what their favorite shoe brand. It is for an Algebra Project due Monday.
Answer:
Keen
Step-by-step explanation:
Favorite shoe brand = Keen
Answer:
Nike
Step-by-step explanation:
Nike shoes are great and comfy
In the sequence $$1,2,2,4,8,32,256, each term (starting from the third term) is the product of the two terms before it. For example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). This sequence can be continued forever, though the numbers very quickly grow enormous! (For example, the $14 term is close to some estimates of the number of particles in the observable universe.) What is the last digit of the $35 term of the sequence
The sequence is recursively defined by
[tex]\begin{cases}a_1 = 1 \\ a_2 = 2 \\ a_n = a_{n-1} a_{n-2} & \text{for } n \ge 3\end{cases}[/tex]
By this definition,
[tex]a_{n-1} = a_{n-2} a_{n-3} \implies a_n = a_{n-2}^2 a_{n-3}[/tex]
[tex]a_{n-2} = a_{n-3} a_{n-4} \implies a_n = (a_{n-3} a_{n-4})^2 a_{n-3} = a_{n-3}^3 a_{n-4}^2[/tex]
[tex]a_{n-3} = a_{n-4} a_{n-5} \implies a_n = (a_{n-4} a_{n-5})^3 a_{n-4}^2 = a_{n-4}^5 a_{n-5}^3[/tex]
[tex]a_{n-4} = a_{n-5} a_{n-6} \implies a_n = (a_{n-5} a_{n-6})^5 a_{n-5}^3 = a_{n-5}^8 a_{n-6}^5[/tex]
and so on.
Recall the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, 21, …}, where the next term in the sequence is the sum of the previous two terms. If [tex]F_n[/tex] is the n-th Fibonacci number, then continuing the pattern above we would arrive at
[tex]a_n = {a_2}^{F_{n-1}} {a_1}^{F_{n-2}} = 2^{F_{n-1}}[/tex]
Notice that the sequence of positive powers of 2 leaves a periodic sequence of residues mod 10 :
[tex]2 \equiv 2 \pmod{10}[/tex]
[tex]2^2 \equiv 4 \equiv 4 \pmod{10}[/tex]
[tex]2^3 \equiv 8 \equiv 8 \pmod{10}[/tex]
[tex]2^4 \equiv 16 \equiv 6 \pmod{10}[/tex]
[tex]2^5 \equiv 2 \times 2^4 \equiv 2 \times 6 \equiv 2 \pmod{10}[/tex]
[tex]2^6 \equiv 2^2 \times 2^4 \equiv 4 \times 6 \equiv 4 \pmod{10}[/tex]
and so on; the period of this sequence of residues is 4.
The period of [tex]F_n[/tex] taken mod 4 is 6 :
[tex]\{1, 1, 2, 3, 5, 8, \ldots\} \equiv \{1, 1, 2, 3, 1, 0, \ldots\} \pmod 4[/tex]
(This follows from the "properties" section in the link in comment. In this case, π(4) = 3/2 × 4 = 6.)
It follows that
[tex]34 \equiv 4 \pmod 6 \implies F_{34} \equiv 3 \pmod 4 \implies 2^{F_{34}} \equiv 2^3 \equiv 8 \pmod{10}[/tex]
which means the last digit of [tex]a_{35}[/tex] is 8.
Pls answer this asap
Answer:
9.5 feet
Step-by-step explanation:
Area of square garden = side length²
⇒ 90 = l²
⇒ l = √90
⇒ l = 3√10
⇒ l = 9.5 feet (nearest tenth)
The length of one side lies between the whole numbers 9 and 10.
Answer:
9 and 10
side length = 9.5 ft (nearest tenth)
Step-by-step explanation:
Area of a square = s² (where s is the side length)
Therefore, if the square garden measures 90 ft², the length of one side will be √90.
To find the two whole numbers that √90 lies between, find the perfect square either side of 90.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...
Therefore, 90 lies between 81 and 100:
⇒ 81 < 90 < 100
Square root the numbers:
⇒ √81 < √90 < √100
⇒ 9 < √90 < 10
Therefore, the length of one side of Grandma's garden is between 9 and 10.
To estimate √90 to the nearest tenth, find the difference between the three numbers:
[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]
As 90 is almost in the middle of 81 and 100,
⇒ √90 = 9.5 (nearest tenth)
According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.
Mrs. thomas wants to put a table in the corner of a room. she considers the measurements of these tables. table 1 length: 1.5 feet width: 2.4 feet diagonal: 3.0 feet table 2 length: 3.2 feet width: 2.8 feet diagonal: 4.0 feet table 3 length: 2.4 feet width: 3.2 feet diagonal: 4.0 feet table 4 length: 2.6 feet width: 1.8 feet diagonal: 3.0 feet the walls forming the corner meet at a 90º angle. which table will fit snugly in the corner? table 1 table 2 table 3 table 4
Table 3 will fit snugly in the corner of the room.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
From the given data we will check the value of the diagonal by applying the Pythagorean theorem.
So by using the Pythagorean theorem:-
D ² = L² + W²
D² = ( 2.4 )² + ( 3.2 )²
D² = ( 5.76 + 10.24 ) = 16
D = √16 = 4 feet
Therefore table 3 will fit snugly in the corner of the room.
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Answer:
Table 3.
Step-by-step explanation:
Person above is correct, I'm takin the test!!
The height of a triangle is 12 centimeters more than its base. The area of the triangle is 189 square centimeters Find the base and height of the tiangle?
Answer:
C
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
so, we know in our case
b(b+12) = 189 cm²
b² + 12b - 189 = 0
let's try to solve this by completing the square.
that means we try to find the expression
(b + k)² + c
that is equal to
b² + 12b - 189
(b + k)² + c = b² + 2kb + k² + c = b² + 12b - 189
so,
2k = 12
k = 6
and then
k² + c = -189
6² + c = -189
36 + c = -189
c = -225
(b + 6)² - 225 = 0
(b + 6)² = 225
b + 6 = 15
b = 9
so, the baseline b = 9 cm.
the height b+12 = 9+12 = 21 cm.
A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a
scale factor of 3/4. Find the perimeter of the preimage, the original triangle, before its
dilation. Round your answer to the nearest tenth, if necessary.
If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.
Then the perimeter of the preimage, the original triangle, before its
dilation will be
Let c be the perimeter of the original triangle.
Then we have
[tex]\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67[/tex]
Then the perimeter of the original triangle is 66.67 units.
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Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)
a. 5x + 9y = -45
c. -9x + 5y = 45
b. 9x + 5y = -45
d. 5x - 9y = 45
Answer:
Step-by-step explanation:
Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)
a. 5x + 9y = -45
c. -9x + 5y = 45
b. 9x + 5y = -45
d. 5x - 9y = 45
Simplify the expression (4x2y3)2
Answer:
8x^2 2y^3
Step-by-step explanation:
The radius of a circle is 1 in. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer:
The circumference is 6.3 in
The circumference of the circle is given by the equation C = 6.3 inches
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the circumference of the circle be represented as C
Now , the equation will be
Let the radius of the circle be r = 1 inch
Now , circumference of circle = 2πr
Substituting the values in the equation , we get
The circumference of the circle C = 2 ( 3.14159 ) x 1
On simplifying the equation , we get
The circumference of the circle C = 6.3 inches
Hence , the circumference of the circle is 6.3 inches
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2x+y=26
x-y=4
Descubra o valor de x e y e explique o processo.
The correct roots of this equation is:
x = 10
y = 6
– This equation is a value substitution system. To solve it, we will: add the terms equal to x, with the sums of the equality.
2x + y = 26
x - y = 4
2x + x = 26 + 4
3x = 30
x = 30/3
x = 10
– Now, let's "take" the first equation of the system, and we'll calculate it, replacing x with its value.
2x + y = 26
2 . 10 + y = 26
20 + y = 26
y = 26 - 20
y = 6
Therefore, the roots of this equation or system is:
x = 10
y = 6
The first number in a pattern is 208. The pattern follows the rule subtract 18. What are the next three numbers? (3 points)
a
195, 183, 172
b
190, 183, 176
c
190, 181, 172
d
190, 172, 154
Answer:
d) 190,172,154
Step-by-step explanation:
208-18=190
190-18=172
172-18=154
Which expression can you use that is equivalent to 5x - 2 ( 15 - x )
Answer:
7x - 30
Step-by-step explanation:
5x -2(15-x)
Distribute -2 to the parenthesis
= 5x -30 +2x
Combine like terms
7x-30
find the value of each of the lettered angles in the diagram below
Answer:
Step-by-step explanation:
Remark
You have an isosceles triangle. That means that the angles opposite the marked sides are equal. So mark the angle on the lower left of the triangle as 50 degrees.
The solution to problem depends on the fact that the sum of the two inside angles of the triangle (each of which is marked as 50 degrees) not supplementary to the exterior angle, are still equal to the exterior angle.
Givens
<1 = 50 degrees
<2 = 50 degrees
Exterior angle = 15x + 25 Substitute the givens into the equation
Equation
<1 + <2 = 15x + 25
Solution
50 + 50 = 15x + 25 Combine the left side
100 = 15x + 25 Subtract 25 from both sides
100 - 25 = 15x + 25 - 25 Combine
75 = 15x Divide both sides by 15
75/15 = 15x/15
5 = x
Answer
<1 = 50 degrees
<2 = 50 degrees
15x + 25 = 75 + 25 = 100
Events a and b are independent. the probability of a occurring is . the probability of b occurring is . what is p(a and b)?
Since events a and b are independent P(a and b) = P(a) × P(b)
To answer the question, we need to know what probability is
What is probability?Probability is the likelihood of an event to occur. The probability of the event P(event) = number of required outcomes/total number of outcomes
Probability of independent eventsIf we have two independent event sa and b that have probabilities of occuring P(a) and P(b) respectively, the probability P(a and b) = P(a) × P(b)
So, P(a and b) = P(a) × P(b)
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HELP ME PLEASE IM GOING TO FAIL!!!
Answer:
-1
Step-by-step explanation:
m= -1
Slope Formula: (y2 - y1) / (x2 - x1)
Point 1 = (4, 3)
Point 2 = (11, -4)
Slope = (-4 - 3) / (11 - 4) = -7 / 7 = -1
Answer: slope = -1
Hope this helps!
51% of a university's freshman class are majoring in Economics. If 4590 students in the freshman class are Economics majors, how many students are in the freshman class?
Answer:
2340
Step-by-step explanation:
4590*.51=2340.9
Because you can not have .9 people, you round down to 2340
2341 students are in the freshman class.
What is percentage?Percentage is defined as ratio expressed as a fraction of 100.
Total no. of students in the freshman Economics majors = 4590
51% students of a university's freshman class,
Let x no. of students in the freshman class,
x = 51/100×(4590)
x = 0.51×(4590)
x = 2340.9
x = 2340.9 ≈ 2341
Hence, 2341 students are in the freshman class.
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Hi! really need help with my math and its due tmrw please helppp Also make sure
to slide over to see the other problems sorry if its glitchy.
Answer:
The value of x is equal to 109
Find the values of x for which the function is continuous.
f(x) =
−3x + 7 if x < 0
x^2 + 7 if x ≥ 0
a.x ≠ 0
b.x ≥ 0
c.x ≥ root square 7
d.all real numbers
e.x ≠ 7
It looks like the given function is
[tex]f(x) = \begin{cases}-3x + 7 & \text{if }x < 0 \\ x^2+7 & \text{if }x \ge0\end{cases}[/tex]
The two pieces of f(x) are continuous since they are polynomials, so we only need to worry about the point at which they meet, x = 0. f(x) is continuous there if
[tex]\displaystyle \lim_{x\to0^-} f(x) = \lim_{x\to0^+} f(x) = f(0) = 7[/tex]
To the left of x = 0, we have x < 0, so f(x) = -3x + 7 :
[tex]\displaystyle \lim_{x\to0^-} f(x) = \lim_{x\to0} (-3x + 7) = 7[/tex]
To the right of x = 0, we have x > 0 and f(x) = x² + 7 :
[tex]\displaystyle \lim_{x\to0^+} f(x) = \lim_{x\to0} (x^2 + 7) = 7[/tex]
So f(x) is continuous at x = 0, and hence continuous for all real numbers.
Please some one help with this question
Answer:
Where is the picture????
